Question

Suppose $ABC$ is a triangle with $3$ acute angle $A,B$ and $C$. The point whose coordinates are $(\cos B-\sin A,\sin B-\cos A)$ can be in the

• A. first and $2nd$ quadrant
• B. second the $3rd$ quadrant
• C. third and $4th$ quadrant
• D. second quadrant only

Answer 1

The correct option is D second quadrant only

$A,B,C$ are acute angle vertices

So, $A+B>=dfrac\pi 2$ & $C+B>\frac{\pi }{2}$

$X$ coordinate of $(\cos B-\sin A,\sin B-\cos A)$ is negative & $Y$ coordinate is positive

So, the point lies in $IInd$ quadrant only.